Re: What would the end velocity be if...?

: finite guy <adamlewis@[EMAIL PROTECTED]
>
: Why is the 'most accurate' method just not used all of the time?

Because it's often simpler to use newtonian expressions, and if you've
only measured to one part in a billion, or if you're only concerned with
modeling situations that you will only be able to verify to one part
in a billion, the extra effort is wasted.  (The "one part in a billion"
is an arbitrary illustrative figure only.)

: Certainly, Newtonian and Einsteinian ideas are regarded somewhat
: 'differently'.  In what way are they really different. 

When you get right down to it, they differ in the coordinate transform
wrt which the laws of physics are invariant.  (Phrasing it that way leads
to wondering why the coordinates matter... they don't, really, but it's
an easy way to see what's going on (or, it seems easy to me).)  This in
turn leads to differing formulas for kinematics and dynamics, in
particular
velocity "addition" (or actually, velocity transforms are mere addition),
and in expressions for momentum and kinetic energy, and other miscelania.
If you simplify the einsteinian expressions by taking the limit as
velocity
approaches zero, they turn into the newtonian ones.

: Would you, if possible, explain why E=mc^2 is a planar equation and
: why the 'plane of time' in it is not conceptualised at all? 

I'm afraid I don't understand why there *should* be a "plane" of time.
Certainly, just because a quantity is multiplied by itself doesn't
really imply there's a "plane" of time.  If it did, then the newtonian
expression for distance covered in a given time at a given acceleration
(ie, the newtonian approximation of d=(1/2)at^2) would involve a "plane
of time", and it doesn't seem necessary.

Or, just consider what acceleration is: velocity per time.  How much
do you speed up in a second.  Since velocity is distance per time,
acceleration has units of disance per time squared.  Again, this has
nothing to do with geometry, except perhaps in a *very* abstract sense.

Similarly, the d^2/t^2 units of "c^2" in E=mc^2, do not imply that there
are two different directions of time, or a geometrical plane.  Now, to get
into "where does the c^2 come from anyways" would be a bit more complex.
In the abstract, it's a matter of units analysis.  Energy has *units*
of mass times velocity squared, for reasons similar to the reason why
acceleratio has units of distance per time squared.  It doesn't have to
do with there being a "plane" involved, it has to do with how you use
things with velocity terms in them to calculate the amount of energy.
Potential energy (in the newtonian approximation) is m*d*a, and kinetic
energy is (1/2)mv^2, for reasons that have nothing to do with "planes".
Instead it has to do with the same reason you get time squared when you
use time and acceleration to calculate distance.


Wayne Throop   throopw@[EMAIL PROTECTED]
   http://sheol.org/throopw